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I know, that question is simple, but i can't understand past perfect clearly enough. There are part of text with gaps:

The chart shows the percentage of people aged 65 and over in the US between 1900 and 2000. In the year 1900 just over 4% of the population was aged over 65. However by 1960 this figure had doubled.

Why this sentence "However by 1960 this figure had doubled." can't be in past tense? for example "However by 1960 this figure doubled". I think, this text in right chronological order. But my book disagree with me=(

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    Your book is correct. Since the sentence refers to a process that began in 1900 was completed in 1960, the past perfect is correct. The clue here is the preposition by. If the population had suddenly doubled in 1960, the sentence would be correct in past simple, but with a different preposition: "However, in 1960 this figure doubled." Jun 26, 2017 at 19:20
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    I understand your point. It is possible to use past tense in both sentences. For instance, However, by 1960 this figure was over 8%, double the 1900 number sounds fine to my ear. It is almost always possible to talk in English using only simple present and simple past (and you might not even need simple future but maybe that, too). However, such constructions are boring and childish. Past perfect is most appropriate and if you don't use past perfect when it is clearly most appropriate why even have past perfect? We could all talk like 6-year-olds instead.
    – Brillig
    Jun 29, 2017 at 18:05
  • In other words, it's because the verb 'double' here has to have the sense of completion and 'up until before that (= by 1960) as a past event.' What makes me wonder is why these people didn't write them as 'answer' down there. :) Let me explain it in grammar point of view.
    – karlalou
    Jul 3, 2017 at 18:23
  • Uh… no. You're being misled. Without context there is no significant difference between “… this figure had doubled" and “… this figure doubled”. Who thinks there is, please post a detailed explanation… Jun 4, 2018 at 23:22

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The chart shows the percentage of people aged 65 and over in the US between 1900 and 2000. In the year 1900 just over 4% of the population was aged over 65. However by 1960 this figure had doubled.

Why this sentence "However by 1960 this figure had doubled." can't be in past tense?

The Perfect, as the name suggests, is about completion.
The Past Perfect is about completion "up until sometime ago," as the present perfect is about completion "up until now."

The part "by 1960 this figure had doubled" is talking about a completion in the past. The expression 'by 1960' has the sense of duration as already commented up there, so it goes well with the perfect form.

Logically speaking, the perfect actually exists to add the sense of completion to the finite verb such as infinitives, participles, and modal verbs because these verbs are tenseless and can not talk about past events by themselves. The perfect itself is also tenseless, and thus it's vague in nature and has the sense of duration. That is why when used with a verb that has tense, it ends up saying 'up until now or sometime ago.'

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